A particle executes simple harmonic oscillations with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is
The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is
Options
(a) π (b) 0.707π (c) zero (d) 0.5π
Correct Answer:
0.5π
Explanation:
Let y = […]
For a simple pendulum performing simple harmonic motion, the time period is plotted against its length. The curve will be
Options
(a) straight line (b) circle (c) parabola (d) ellipse
Correct Answer:
parabola
The total energy of a simple harmonic oscillator is proportional to
Options
(a) square root of displacement (b) velocity (c) frequency (d) square of amplitude
Correct Answer:
square of amplitude
Explanation:
The total […]
A particle of mass M is executing oscillations about the origin on the x-axis. The potential energy is U(x)=k|x|³, where k is a positive constant. If the amplitude of oscillation is a, then its time […]
A point performs simple harmonic oscillation of period T and the equation of motion is given by x=a sin(ωt+π/6). After the elapse of what fraction of the time period the velocity of the point will […]
The particle executing simple harmonic motion has a kinetic energy K₀ cos²ωt. The maximum values of the potential energy and the total energy are respectively
Options
(a) K₀/2 and K₀ (b) K₀ and […]
A thin wire of length L and mass M is bent to form a semicircle. What is the gravitational field at the centre?
Options
(a) πGM/L² along the line joining the ends (b) […]
A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is
Options
(a) 4 Hz (b) 3 Hz (c) 2 Hz (d) 1 […]
The potential energy of a simple harmonic oscillator when the particle is half way to its end point is (where E is the total energy)
Options
(a) E/8 (b) E/4 (c) E/2 (d) 2E/3
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